# Closure (topology): Difference between revisions

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[[ | In [[mathematics]], the '''closure''' of a subset ''A'' of a [[topological space]] ''X'' is the set union of ''A'' and ''all'' its [[topological space#Some topological notions|limit points]] in ''X''. It is usually denoted by <math>\overline{A}</math>. Other equivalent definitions of the closure of A are as the smallest [[closed set]] in ''X'' containing ''A'', or the intersection of all closed sets in ''X'' containing ''A''. | ||

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## Revision as of 05:09, 26 September 2007

In mathematics, the **closure** of a subset *A* of a topological space *X* is the set union of *A* and *all* its limit points in *X*. It is usually denoted by . Other equivalent definitions of the closure of A are as the smallest closed set in *X* containing *A*, or the intersection of all closed sets in *X* containing *A*.